Hamiltonian Approach to QCD: The effective potential of the Polyakov loop

TL;DR

This paper develops a Hamiltonian framework to compute the effective potential of the Polyakov loop in Yang-Mills theory, revealing insights into confinement and deconfinement transitions with a critical temperature of 270 MeV for SU(2).

Contribution

It introduces a Hamiltonian approach with background gauge fixing to analytically relate finite and zero temperature propagators, and calculates the deconfinement critical temperature non-perturbatively.

Findings

Derived the effective potential for the Polyakov loop.

Established an analytic relation between finite and zero temperature propagators.

Estimated the deconfinement critical temperature as 270 MeV for SU(2).

Abstract

The effective potential of the order parameter for confinement is calculated within the Hamiltonian approach to Yang--Mills theory. Compactifying one spatial dimension and using a background gauge fixing this potential is obtained by minimizing the energy density for a given background field. Using Gaussian type trial wave functionals I establish an analytic relation between the propagators in the background gauge at finite temperature and the corresponding zero temperature propagators in Coulomb gauge. In the simplest truncation, neglecting the ghost and using the ultraviolet form of the gluon energy one recovers the Weiss potential. From the fully non-perturbative potential (with the ghost included) one extracts a critical temperature of the deconfinement phase transition of 270 MeV for the gauge group SU(2).